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Biometrics & Biostatistics International Journal
Retrospective Assessment of Non-Inferiority in the Rare
Disease, Guillain–Barre Syndrome
Abstract
Research Article
Background: Non-inferiority testing is used to demonstrate that a new treatment
is not unacceptably worse than an existing treatment. Such analyses are useful, for
example when placebo-controlled studies are unethical, or when there may be other
considerations (e.g. convenience, cost) where the new treatment has an advantage.
Prospective, non-inferiority trials in orphan diseases are difficult to coordinate
because they often require large sample sizes to detect small margins of difference
between treatments. In this report, we present a retrospective study of non-inferiority
testing in the rare disease, Guillain–Barre syndrome (GBS).
Methods: Meta-analysis results of PE versus a control group (n=623) were used to
derive non-inferiority margins for two endpoints:
I. Improvement of ≥1 grade on the GBS disability scale,
II. Mean change from baseline on the GBS disability scale.
Volume 1 Issue 2 - 2014
Chunqin Deng*, Junliang Chen and Kim
Hanna
Grifols Therapeutics Inc., USA
*Corresponding author: Chunqin Deng, 79 TW
Alexander Drive, Durham, North Carolina, USA, Tel: 1
919-316-6440; Email:
Received: October 10, 2014 | Published: November
08, 2014
These were then retrospectively applied to meta-analysis results to demonstrate the
non-inferiority of IVIg to PE (n=567).
Results: For endpoint 1, the non-inferiority margin of the risk ratio was 0.865. The
risk ratio of IVIg versus PE was 1.08 (95% confidence interval [CI]: 0.94 to 1.23). Since
the lower bound of the CI is above the non-inferiority margin (0.865), IVIg can be
considered non-inferior to PE on this endpoint. For endpoint 2 assessing change from
baseline on GBS disability scale, the non-inferiority margin was 0.315. The treatment
difference (IVIg – PE) was -0.02 (95% CI: -0.25 to 0.20). Since the upper bound of 95%
CI (0.20) is less than 0.315 (the non-inferiority margin), IVIg can be considered noninferior to PE.
Conclusion: The results demonstrate non-inferiority of IVIg to PE in GBS when the
non-inferiority margins are retrospectively applied. Retrospective non-inferiority
analyses may also be used in evaluation of treatment effects for other rare diseases.
Keywords
Non-inferiority margin; Orphan disease; Guillain–Barre syndrome; Plasma exchange
(PE); Intravenous immunoglobulin (IVIg)
Background
Randomized, placebo-controlled trials are the standard
method by which the efficacy of medical treatments is determined.
However, in serious diseases where there is a known effective
treatment, allocating one patient group to a placebo arm may be
unethical. Furthermore, in some situations, a new treatment may
not be expected to be more effective than an existing treatment
on the primary endpoint, but may have advantages in terms of
secondary endpoints, such as safety, convenience, compliance or
cost [1,2]. The non-inferiority trial is a vital tool when evaluating
the efficacy of a novel therapy compared with an existing therapy.
It aims to demonstrate that the test product is not worse than
the comparator by more than a pre-specified, small amount. This
amount is known as the non-inferiority margin, or delta (Δ) [1].
Guidelines developed by the European Medicines Agency and the
US Food and Drug Administration [3] recommend predefining
the non-inferiority margin. This margin can be derived from
previous studies using historical data, and the study medication is
typically expected to retain at least 50% of the original treatment
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effect over placebo or the standard of care to be considered noninferior.
After a non-inferiority margin is established, a prospective
non-inferiority trial is usually conducted to confirm the noninferiority of the new product when compared to the existing
product. Non-inferiority trials typically require considerably
larger sample sizes than placebo-controlled trials [4]. This is
due to the fact that the margin of equivalence (non-inferiority)
is often much smaller than the treatment difference, which a
placebo-controlled trial must be powered to detect. It is therefore
important for non-inferiority trials to have large sample sizes,
and for this reason, trials of orphan drugs in rare diseases face
significant challenges in terms of recruiting sufficient sample
sizes to formally assess prospectively defined non-inferiority and
of completing the trial within a realistic timeframe.
Here, we present a practical method for demonstrating noninferiority of drugs for rare disease. This method is based on
aggregated data from smaller studies that have been analyzed in
previously published meta-analyses [5,6], and is illustrated using
Biom Biostat Int J 2014, 1(2): 00009
Retrospective Assessment of Non-Inferiority in the Rare Disease, Guillain–Barre Syndrome
the example of intravenous immunoglobulin (IVIg) compared
with plasma exchange (PE) for the treatment of Guillain–Barre
syndrome (GBS).
GBS is a rare inflammatory disease affecting the peripheral
nerves and causing weakness, numbness, breathing difficulty
and paralysis. The disease affects between 0.5 and 2 per 100,000
persons per year [6]. Although still under investigation, the cause
of GBS is believed to be an autoimmune response [5,6]. In some
patients, the condition can have a lasting impact after the end
of its acute phase [5]. Supportive care for GBS can include the
administration of heparin, and the use of pressure stockings to
prevent the onset of deep vein thrombosis in bed-bound patients,
along with the monitoring of pulse, blood pressure, autonomic
disturbances and respiration. Rehabilitation focuses on exercise
to encourage strengthening, proper limb positioning, posture
and orthotics [7].
There are two effective immune therapies for GBS: PE, which
involves separation of plasma from cells and re-infusion of
those cells back into the patient, and IVIg, which uses antibodies
purified from plasma that has been pooled from at least 1000
donors [5,6]. Administering IVIg is simple compared with PE. PE
requires access to two veins, of which one has to permit high flow
volumes, and frequently necessitates the insertion of a central
venous line, a PE machine and specially trained personnel. IVIg
requires access to only a single peripheral vein and no special
equipment or specially trained staffs are necessary. Consistent
with the difference in ease of administration, a Cochrane Review
found that the risk ratio (RR) of treatment being discontinued
was 0.14 less in the IVIg than in the PE group (95% confidence
interval [CI]: 0.05 to 0.36). In addition, there is some evidence
that adverse events are more frequent with PE than IVIg [5].
The clinical benefits of PE in GBS as measured by
improvement on the GBS disability scale developed by Hughes
et al. [8] have been confirmed in a Cochrane Review [6], which
included six randomized, controlled trials (RCTs) [9-14]. Few
trials comparing IVIg with placebo have been conducted because
PE was the standard of care when IVIg was introduced for GBS.
However, a number of studies [15-21] show that IVIg speeds
recovery from GBS to a similar extent as PE, as concluded by a
Cochrane Review [5].
Due to the rarity of GBS, the majority of studies comparing
IVIg and PE has used small sample sizes with limited statistical
power and were not formally designed as therapeutic
equivalence or non-inferiority trials [5]. This may help to explain
some inconsistency in the findings, and it is possible that some
studies finding no significant difference between treatments
reflect a lack of power to detect a significant difference rather
than indicating true non-inferiority. The Cochrane Review by
Hughes et al. [5] thoroughly reviewed all individual studies
and performed a meta-analysis, but did not formally assess
therapeutic equivalence or non-inferiority. The conclusion of
no treatment difference cannot be automatically translated into
either equivalence or non-inferiority.
Given the strong safety profile of IVIg [22], as well as the
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convenience of its use in the clinic [15], the current analysis was
undertaken to formally establish the non-inferiority of IVIg to PE
using existing studies from comparisons of PE versus supportive
care, where much more data are available. A Cochrane Review
of the benefits of PE in GBS [6] was used to establish the noninferiority margin, and then this derived non-inferiority margin
was retrospectively applied to results from an existing, most
recent Cochrane Review of IVIg benefits in GBS [5] to demonstrate
the non-inferiority of IVIg to PE.
Methods
In non-inferiority trials, one of the critical steps is to define
the non-inferiority margin. This margin can be derived from
previous studies using historical data, and the study medication is
typically expected to retain at least 50% of the original treatment
effect over placebo or the standard of care to be considered noninferior. In the example in GBS, the non-inferiority margin was
derived using results from the meta-analysis of previous trials
comparing PE versus supportive care.
Raphael et al. [6] conducted a meta-analysis of five studies
(623 subjects; a summary of the included trials is shown in
(Table 1). The RR of PE versus supportive care for the proportion
of subjects with improvement of at least one grade on the GBS
disability scale was calculated as 1.64 (95% CI: 1.37 to 1.96)
(Table 2). For the proportion of subjects with improvement of
at least one grade on the GBS disability scale, the non-inferiority
margin for the RR can be derived using the fixed-margin method
or the two 95% CI approach [1,3,23-24]. For the purposes of
this study, the new treatment is IVIg and the active control is PE.
The fixed-margin approach involves determining the treatment
effect (M1) of the active control group over the placebo (or no
treatment) group by using the lower bound (or upper bound,
depending on the direction) of the 95% CI from previous placebocontrolled trials or meta-analyses of trials. i.e., M1 = 1.37 which is
the lower limit of 95% CI of the RR. Typically, preserving at least
50% of M1 from active control versus placebo (or no treatment)
is recommended [3]. i.e., RR of IVIg versus no treatment is greater
or equal to 1 + ( M 1 − 1) × 50% = 1.185 . The non-inferiority margin
(M2) is then derived by ensuring that the lower bound (or upper
bound, depending on the direction) of the 95% CI is >M2. i.e., RR
1.185
= 0.865 .
1.37
A further meta-analysis was also performed on four studies
(585 subjects) (Table 2) to assess change from baseline to Week
4 using the GBS disability scale (endpoint 2). The treatment
difference (PE – supportive care) was calculated as -0.89 (95%
CI: -1.14 to -0.63) [6]. For the mean change from baseline on the
GBS disability scale, the non-inferiority margin for the treatment
difference can be derived using the fixed-margin method or the
two 95% CI approach [1,3,23-24]. The fixed-margin approach
involves determining the treatment effect (M1) of the active
control group over the placebo (or no treatment) group by using
the upper bound (or lower bound, depending on the direction)
of the 95% CI from previous placebo-controlled trials or metaanalyses of trials. i.e., M1 = -0.63 which is the upper limit of 95%
of IVIg versus PE is greater than M 2 =
Citation: Deng C, Chen J, Hanna K (2014) Retrospective Assessment of Non-Inferiority in the Rare Disease, Guillain–Barre Syndrome. Biom Biostat
Int J 1(2): 00009. DOI: 10.15406/bbij.2014.01.00009
Retrospective Assessment of Non-Inferiority in the Rare Disease, Guillain–Barre Syndrome
Table 1: Trials of PE versus supportive care included in meta-analysis of endpoint 1 and 2 [6].
Greenwood [11]
McKhann [9]
Osterman [12]
Raphael [13]
Raphael [14]
Trial design
RCT, multicentre,
open, parallel
groups
Participants
n=29, acute GBS only
All ages
No mild forms
RCT, multicentre,
open, parallel
groups
n=245, acute GBS only
All ages
No mild forms
RCT, multicentre,
open, parallel
groups
n=220, acute GBS only
Adults only
All forms
RCT, multicentre,
open, parallel
groups
RCT, multicentre,
open, parallel
groups
n=38, acute GBS only
Adults only
No mild forms
n=91, acute GBS only
Adults only
Mild forms
Interventions
PE versus supportive care
Five PE in 10 days, 55 mL/
kg per PE
PE versus supportive care
Three to five PE in 5 days, 40
mL/kg per PE
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Endpoint
PE versus supportive care
Three to eight PE in 7 to 10
days, 3 L per PE
PE versus supportive care
Four PE in 8 days, 3 L per PE,
diluted albumin or fresh
frozen plasma
PE versus supportive care
Two PE every other day, 3 L
per PE, diluted
GBS: Guillain-Barre syndrome; PE: Plasma Exchange; RCT: Randomised Controlled Trial, SD: Standard Deviation
Table 2: Meta-analysis results and derivation of M1 and M2.
PE
Control (supportive care)
Statistical test
Point estimate (95% CI)
M1 (PE/Control)
Endpoint 1: The proportion of subjects with improvement by at least one grade after 4 weeks
1.64
176/308 (57.1%)
110/315 (34.9%)
Risk ratio
1.37
(1.37 to 1.96)
Endpoint 2: Mean disability grade improvement after 4 weeks
-0.89
N=290
N=295
Mean difference
-0.63
(-1.14 to -0.63)
CI: Confidence Interval; IVIg: Intra Venous Immunoglobulin, PE: Plasma Exchange
CI of the treatment difference. Preserving at least 50% of M1 from
active control versus placebo (or no treatment) is recommended
[3]. i.e., treatment difference of IVIg - no treatment is less or
equal to M 1 × 50% = −0.315 . The non-inferiority margin (M2) is
then derived by ensuring that the upper bound (or lower bound,
depending on the direction) of the 95% CI is < M2. i.e., treatment
difference of IVIg - PE is less than M 2 = −0.315 − ( −0.63) = 0.315 .
The detailed derivation is shown below.
Results
Endpoint 1: Improvement of at least one grade on the
GBS disability scale
The treatment effect (M1) for PE versus Control (supportive
care) is defined as the lower limit of the 95% CI of the RR.
M1 =
P ( PE )
= 1.37 (i.e. lower limit of CI ) (Table 2), where P
P (Control )
is proportion of subjects with improvement of at least one grade
on the GBS disability scale. Assuming a need to preserve 50% of
the treatment effect of PE versus Control to show that IVIg is noninferior to PE, the treatment effect of IVIg must be:
P ( IVIg )
= 1 + (1.37 − 1) × 50% = 1.185
P (Control )
The non-inferiority margin (M2) for IVIg versus PE can be
calculated as follows:
1, 2
1, 2
1
1, 2
1, 2
M2 (IVIg/PE)
0.865
0.315
 P ( IVIg )

P ( IVIg ) 
1.185
P (Control ) 
=
=
= 0.865
 P ( PE )
 1.37
P ( PE )
P (Control ) 

Therefore, the non-inferiority margin of the RR is 0.865, and
IVIg is non-inferior to PE if the lower bound of the 95% CI of the
RR of IVIg versus PE is greater than 0.865.
Hughes et al. [5] conducted a meta-analysis of six studies
(567 subjects) [15-20]. An overview of the trials included is given
in (Table 3). The RR of IVIg versus PE was 1.08 (95% CI: 0.94
to 1.23) for the proportion of subjects with improvement of at
least one grade on the GBS disability scale. Since the lower bound
of the 95% CI (0.94) is above the non-inferiority margin (0.865),
IVIg can be considered non-inferior to PE on this endpoint (Table
4).
Endpoint 2: Mean change from baseline on the GBS
disability scale
The non-inferiority margin can be derived using the two 95%
CI approach [1,23]. Treatment effect (M1) for PE versus Control
(supportive care) is defined as the upper limit of 95% CI of
treatment difference.
M 1 = PE − Control = −0.63 (i.e. upper limit of CI) (Table 2)
To demonstrate non-inferiority of IVIg versus PE, the
treatment effect of IVIg must preserve 50% of M1.
Citation: Deng C, Chen J, Hanna K (2014) Retrospective Assessment of Non-Inferiority in the Rare Disease, Guillain–Barre Syndrome. Biom Biostat
Int J 1(2): 00009. DOI: 10.15406/bbij.2014.01.00009
Retrospective Assessment of Non-Inferiority in the Rare Disease, Guillain–Barre Syndrome
IVIg − Control = −0.63 × 50% = −0.315
The non-inferiority margin (M2) for IVIg versus PE is
calculated as follows:
IVIg − PE = ( IVIg − Control ) − ( PE − Control ) = −0.315 − (−0.63) = 0.315
Therefore, 0.315 is the non-inferiority margin for the mean
change from baseline on the GBS disability scale. IVIg can be
considered non-inferior to PE if the upper bound of the 95% CI of
mean difference of IVIg versus PE is less than 0.315.
Hughes et al. [5] Conducted a meta-analysis of five studies
(536 subjects) (Table 3) [15-17,19-20]. The treatment difference
(IVIg – PE) was -0.02 (95% CI: -0.25 to 0.20). Since the upper
bound of 95% CI (0.20) is less than 0.315 (the non-inferiority
margin), IVIg can be considered non-inferior to PE (Table 4).
Discussion
This analysis provides an illustration of how data collected
from a number of small studies may be used to enable
retrospective non-inferiority comparisons of treatments for
rare diseases, for which it is often impossible to have adequate
sample sizes for prospectively designed non-inferiority studies.
In the example analysis presented here, the treatment effect of
IVIg for GBS was compared with that of an established treatment
(PE) for this condition with efficacy proven in RCTs. Based on this
evaluation; we can conclude that IVIg is non-inferior to PE for the
treatment of GBS.
Table 3: Trials of IVIg versus PE included in meta-analysis of endpoints 1 and 2 [5].
Trial design
Randomized,
national,
multicentre,
parallel group
van der Meche [20]
PSGBS Study Group [15]
Diener [17]
Nomura [19]
El-Bayoumi [18]
Participants
Interventions
Endpoint
Adults and children
N=150
IVIg 0.4 g/kg daily for 5 days
versus PE 200 to 250 mL/kg
over 7 to 14 days
1, 2
IVIg 0.5 g/kg daily for 4 days
versus PE 40 to 50 mL/kg
on five occasions over 7 to
10 days
Randomized,
IVIg 0.4 g/kg daily for 5
international,
Adult
days versus PE 250 mL/kg
multicentre,
N=383
over 8 to 13 days versus PE
parallel group
followed by IVIg
IVIg 0.4 g/kg daily for 5
days versus PE 40 to 50 mL/
kg on five occasions within
Randomized,
Adults (possibly children)
14 days versus immune
multicentre,
N=74
absorption on five occasions
parallel group
(4000 mL on two occasions
and then 2000 mL on three
occasions) within 14 days
IVIg (Teijin brand) 0.4 g/kg
Randomized,
daily for 5 days versus PE
Adult
multicentre,
total 200 to 250 mL/kg in
N=47
parallel group
up to seven sessions over 4
weeks
IVIg 0.4 g/kg daily for 5 days
Children (age not specified)
Open, parallel-group,
versus one plasma volume
with GBS requiring artificial
randomized, controlled trial
PE daily for 5 days
ventilation
Randomized,
single-centre,
parallel group
Bril [16]
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Adult
N=50
1, 2
1, 2
1, 2
1, 2
1
GBS: Guillain–Barre syndrome; IVIg: Intravenous Immunoglobulin; PE: Plasma Exchange; PSGBS: Plasma Exchange/Sandoglobulin Guillain–Barre
Syndrome
Table 4: Meta-analysis results and determination of non-inferiority.
IVIg
177/293 (60.4%)
N=273
Point estimate (95%
Non-inferiority margin
Non-inferiority of IVIg
CI)
(M2)
versus PE
Endpoint 1: The proportion of subjects with improvement by at least one grade after 4 weeks
1.08
154/274 (56.2%)
Risk ratio
0.865
Yes
(0.94 to 1.23)
Endpoint 2: Mean disability grade improvement after 4 weeks
-0.02
N=263
Mean difference
0.315
Yes
(-0.25 to 0.20)
PE
Statistical test
CI: Confidence Interval; IVIg: Intravenous Immunoglobulin; PE: Plasma Exchange
Citation: Deng C, Chen J, Hanna K (2014) Retrospective Assessment of Non-Inferiority in the Rare Disease, Guillain–Barre Syndrome. Biom Biostat
Int J 1(2): 00009. DOI: 10.15406/bbij.2014.01.00009
Retrospective Assessment of Non-Inferiority in the Rare Disease, Guillain–Barre Syndrome
Post-hoc analyses of non-inferiority have limitations, such
as differences in study design, treatment regimens and patient
characteristics across trials. Ideally, a prospective clinical trial
should be undertaken to assess the non-inferiority of IVIg.
However, based on the derived non-inferiority margin in this
study, a sample size of more than 462 subjects would be needed
without drop out consideration to conduct a prospective clinical
trial to assess the non-inferiority of IVIg versus PE with 80%
power for endpoint 1 assuming a rate of 60% for IVIg and
56% for PE. Similarly, a sample size of more than 622 subjects
would be needed without drop out consideration to conduct
a prospective clinical trial to assess the non-inferiority of IVIg
versus PE with 80% power for endpoint 2 assuming no treatment
difference between IVIg and PE and standard deviation of 1.4 for
both treatments, which would be a considerable challenge for
a disease that is as rare as GBS. In addition, since the previous
studies have showed the benefit of the IVIg in treating GBS,
it is quite challenging for a sponsor to perform a large scale,
prospective non-inferiority study. Instead, this retrospective
assessment make use of the most recent Cochrane reviews based
on previously collected data, permitting non-inferiority of IVIg
compared with PE to be demonstrated.
A 1997 study conducted by the Plasma Exchange/
Sandoglobulin Guillain–Barre Syndrome (PSGBS) Trial Study
Group established that IVIg is therapeutically equivalent to PE.
Treatments were considered equivalent if the 95% CI of the
difference in mean improvement in GBS disability scale after 4
weeks between the two groups excluded a true mean difference
of more than 0.5 of a grade. Although a change of 1.0 of a grade
could be reliably measured and was clinically meaningful, a
mean change of less than 0.5 of a grade was considered to be
insignificant; however this equivalence value is subjective, and is
not based on data from randomized clinical trials. In the current
study, a non-inferiority margin of 0.315 of a grade was derived
using retrospective data; this is therefore more stringent than
the equivalence margin of 0.5 of a grade used in the PSGBS Study
Group study [15].
This study demonstrates that, in the case of rare diseases
where formal prospective non-inferiority design is rendered
unfeasible by the large sample sizes required, retrospective
data analyses can be undertaken to ascertain whether a new
treatment meets criteria for non-inferiority. We recommend that
this strategy be considered in other orphan diseases as a practical
means to establish non-inferiority of treatment efficacy when
prospectively designed non-inferiority studies are not feasible.
Conclusion
Using the example from GBS, this study presents practical
methodology for retrospective non-inferiority analyses which
can be used in evaluation of treatments for rare diseases where
formal, prospective non-inferiority studies are not possible.
Competing Interests
The authors are all employees of Grifols Inc., manufacturer of
Gamunex®-C and Flebogamma® (both IVIg products).
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Authors’ contributions
CD and KH initiated the idea for developing this paper. CD
and JC carried out the calculations and performed the statistical
analysis. CD drafted the manuscript, the final version of which
was reviewed and approved by all authors.
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Int J 1(2): 00009. DOI: 10.15406/bbij.2014.01.00009
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Citation: Deng C, Chen J, Hanna K (2014) Retrospective Assessment of Non-Inferiority in the Rare Disease, Guillain–Barre Syndrome. Biom Biostat
Int J 1(2): 00009. DOI: 10.15406/bbij.2014.01.00009